MINEOLA, L.I., April 26— Nassau County's most powerful Republican, Joseph N. Mondello, said today that he was stepping down from the County Board of Supervisors to become chairman of the Nassau Offtrack Betting Corporation, but would remain the leader of the county's Republican Party. 
The $139,000-a-year OTB position, regarded as a rich patronage plum, was essentially Mr. Mondello's for the asking, since he largely controls patronage in this Republican-dominated county.
The new post will give Mr. Mondello ample time to focus on political matters as Republicans are facing the strongest challenge for control of the county's government in more than 70 years.
Although Mr. Mondello had hinted at an interest in the OTB job, his announcement at a Board of Supervisors meeting here still caught colleagues by surprise. At his request, the board unanimously approved a measure naming Mr. Mondello to the Nassau OTB board, a prerequisite to a vote by the OTB board electing him chairman. Foes See Challenge 
Mr. Mondello, 55, a lawyer from Levittown, earns $39,500 as a member of the Board of Supervisors, a position he has held for six and a half years. He has been chairman of the county's Republican Party since May 1983. 
Political opponents said today that Mr. Mondello's hold on the party leadership had weakened, and they predicted he would face a challenge for the party post, which pays $75,000 and includes a free car. "There's going to be a fight now," said a Democratic board member, Benjamin L. Zwirn, supervisor of the Town of North Hempstead. 
But Mr. Mondello dismissed that as "wishful thinking," and said he was leaving elected office at a time when "my leadership of the party has never been stronger." 
"I always admired Rocky Marciano and Joe DiMaggio," he said. "They went out while they were on top. Everyone who has left this board has done it with a whimper. I got a standing ovation." 
Mr. Mondello said he expected to be named to the OTB position by the corporation's board today after the resignation on Friday of the current chairman, Easa Easa. He said he had considered seeking the job "for some time," and made his decision over the weekend. He said he would announce at a meeting of the Hempstead Town Board Tuesday morning that he was also relinquishing the $60,500-a-year post as the town's presiding supervisor. The town board will name his successor. Erosion of G.O.P. Power 
During Mr. Mondello's tenure, Republicans who long ruled Nassau lost political control of the Board of Supervisors, where Democrats now hold nearly equal power. 
His announcement today coincides with a Federal judge's order directing the county to offer plans within 45 days for replacing its Board of Supervisors. The judge, Arthur D. Spatt of Federal District Court in Uniondale, declared the board unconstitutional in a ruling on Tuesday because its weighted voting system violated the principle of one person one vote. 
Mr. Mondello said the replacement of the board by a county legislature would benefit Republicans and was not a factor in his decision to step down.
Thomas S. Gulotta, the County Executive and a Republican, praised Mr. Mondello for "years of public service" despite a rift between the two top Republicans over taxes and the county budget.
But Mr. Zwirn blamed the Republican chairman for property-tax increases. "The only issue is taxes, and I think Mr. Mondello recognized what was going to happen this fall," Mr. Zwirn said. "So he found himself the safest patronage job he could find."